Question

In: Electrical Engineering

The voltage and current at the terminals of a network are v=30+56cos2000t+20sin8000tV, i=3+5cos(2000t−25∘)+sin(8000t+45∘)A. The current is...

The voltage and current at the terminals of a network are
v=30+56cos2000t+20sin8000tV,
i=3+5cos(2000t−25∘)+sin(8000t+45∘)A.
The current is in the direction of the voltage drop across the terminals.

Part A

What is the average power at the terminals?

Express your answer to three significant figures and include the appropriate units.

Part B

What is the rms value of the voltage?

Express your answer to three significant figures and include the appropriate units.

Part C

What is the rms value of the current?

Express your answer to three significant figures and include the appropriate units.

Solutions

Expert Solution

The above explained procedure to find RMS voltage, current and average power is a generic one. It can be applied to any number of frequency components.


Related Solutions

The output voltage of an AC generator is given by V = (1.20×10^2) sin (30 pie...
The output voltage of an AC generator is given by V = (1.20×10^2) sin (30 pie t) (V). The generator is connected across a 0.500 H inductor. Find the (a) frequency of the generator, (b) rms voltage across to the inductor (c) inductive reactance, (d) rms current in the inductor, (e) maximum current Indian doctor, and (f) average power delivered to the inductor. (g) find an expression for instantaneous current. (h) At what time after t = 0, does the...
P = Power, V = Voltage, I = Current, and R = Resistance. Which of the...
P = Power, V = Voltage, I = Current, and R = Resistance. Which of the following relations is incorrect? Choices: V = I R P = V R P = VI I = V/R
The output voltage of an AC generator is given by ?v = 121 V sin (32?t)....
The output voltage of an AC generator is given by ?v = 121 V sin (32?t). The generator is connected across a 0.007 H inductor. Find the following. (a) frequency of the generator?=____ Hz (b) rms voltage across the inductor?=____ V (c) inductive reactance?=____ ohms (d) rms current in the inductor?=____ A (e) maximum current in the inductor?=____ A (f) average power delivered to the inductor?=____ W (g) Find an expression for the instantaneous current. (Use the following as necessary:...
a)The voltage and the current of a circuit are v=1∠30oV and i=2∠-37oA. Determine the power factor....
a)The voltage and the current of a circuit are v=1∠30oV and i=2∠-37oA. Determine the power factor. b)A short transmission line is delivering a 3-phase load of 1MVA at 11kV and the load power factor is 0.8 lagging. The total series impedance of the line is (10 + j20)Ω/phase. Calculate the sending end power factor. c)A supply company offers a Two-parts Tariff on a monthly basis. The Maximum Demand Charge is $90 per kVA per month and the Energy Charge is...
1. A voltage is given by v(t) = 10 sin(1000?t + 30o). a. Use a cosine...
1. A voltage is given by v(t) = 10 sin(1000?t + 30o). a. Use a cosine function to express v(t). b. Find the angular frequency, the frequency in hertz, the phase angle, the periodic time and the rms value. c. Find the power that this voltage delivers to a 25? resistance
A. According to Equation 20.7, an ac voltage V is given as a function of time t by V = Vo sin 2ft, where Vo is the peak voltage and f is the frequency (in hertz).
  A. According to Equation 20.7, an ac voltage V is given as a function of time t by V = Vo sin 2ft, where Vo is the peak voltage and f is the frequency (in hertz). For a frequency of 56.0 Hz, what is the smallest value of the time at which the voltage equals one-half of the peak-value? B. The rms current in a copy machine is 7.36 A, and the resistance of the machine is 19.8Ω. What...
Consider a simple RL circuit consisting of an ideal battery with voltage 30 V , a...
Consider a simple RL circuit consisting of an ideal battery with voltage 30 V , a resistor of resistance 15 Ω, an inductor of inductance 7.0 H, and a switch all in series. The switch is initially open. a) Determine the ratio of the voltage across the resistor to the voltage across the inductor when the current has a value of 1.5 A. b) How much time has elapsed if the voltage across the resistor is 20 V ?
"Hit" Group "Smashed Into" Group 25 50 25 45 34 55 30 40 36 45 37...
"Hit" Group "Smashed Into" Group 25 50 25 45 34 55 30 40 36 45 37 41 31 50 35 35 30 37 35 45 30 55 25 50 20 45 25 43 30 42 24 40 34 36 33 45 37 50 38 41 A. Null Hypothesis? Ha: Smashed into group estimated higher speed than hit group Ho: Smashed into group estimated lower or same speed than hit group(directional hypothesis) B. Alternative hypothesis? Ha: Smashed into group estimated higher...
Table 2: Voltage Readings of Different AA Battery Combinations Battery Combination Voltage (V) Current (A) 1...
Table 2: Voltage Readings of Different AA Battery Combinations Battery Combination Voltage (V) Current (A) 1 1.58 1.4 1 and 2 3.16 3.37 1, 2 and 3 4.74 4.50 1, 2, 3 and 4 6.50 6.17 Table 3: Resistor Data Resistance (Ω) Slope (V/A) Percent Difference 10 Plot a graph of Table 2. Consider which variable (voltage or current) should be on the x and y axes. What is the relationship between voltage and current? Use data from your graph...
A blow-dryer and a vacuum cleaner each operate with a voltage of 120 V. The current...
A blow-dryer and a vacuum cleaner each operate with a voltage of 120 V. The current rating of the blow-dryer is 9.2 A, while that of the vacuum cleaner is 5.9 A. Determine the power consumed by (a) the blow-dryer and (b) the vacuum cleaner. (c) Determine the ratio of the energy used by the blow-dryer in 18 minutes to the energy used by the vacuum cleaner in 56 minutes.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT